Help with a study guide question, i will give best response. (Attached file.) Please Help me! I'm study for a big test

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Help with a study guide question, i will give best response. (Attached file.) Please Help me! I'm study for a big test

Mathematics
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apply distributive property where possible distributive property says a(b+c) is equal to ab+ac I see you have 3(x-y) apply distributive property there
you can tell me what you get when you apply distributive property to 3(x-y)?

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3xy? or 3(y-x) p Idk how to do the distributive property
you do see distributive property is a(b+c)=ab+ac we are taking the outer number and multiplying it to both terms inside the ( )?
example 6(2+7) is the same as 6*2+6*7 though we didn't need distributive property here because we know what 2+7 is... 6(2+7)=6(9)=54 but we see we get the same number using the distributive property 6(2+7)=6*2+6*7=12+42=54
here we can't do y take away x because we don't know what x and y are so you have to apply distributive property here where you have 3(x-y)
3(x-y) is the same as 3x-3y
\[3x+4y+3(x-y)-4x \\ 3x+4y+3x-3y-4x\]
now using that addition is commutative to place like terms together
commutative property is just changing the order
so for the first slot it's written like 3x+4y+3x-3y-4y = Distributive property??
almost
you want to leave that last term as it was we didn't do anything to it
Umm, how do you write exactly? I'm a little lost on what your saying...sorry
should be 3x+4y+3x-3y-4x by use of the distributive property
-4x doesn't just turn into -4y
Oh! I got it! Okay give me a sec to write it, and then we can move to the next slot?
I got it! so next one?
have you tried changing the order to put like terms together yet? that was what I suggested above.... I also gave the name of this property too. :) You try it and I will check it.
Wait, what do you want me to do?
change the order so like terms are together
like terms are terms with the same variable part
you should see three terms that have the common variable x you should see two terms that have the common variable y
put all your x terms together and put all your y terms together
10x +7y Like that?
like if I had a+a+b+a+b-4a reorder so that like terms are together a+a+a-4a+b+b
3x+3x+4x=10x 4y+3y=7
^^ That?
you shouldn't change the sign in front of the term you had 3x+4y+3x-3y-4x by commuative property we can write this as 3x+3x-4x+4y-3y
Oh... I was supposed to add all the X's in order, and all the y's after that?
Example: \[a+a+b+a+4(\frac{1}{4}b-a) \text{ given } \\ a+a+b+a+4 \cdot \frac{1}{4} b-4a \text{ by distributive property } \\ a+a+b+a+b-4a \text{ by simplification } \\ a+a+a-4a+b+b \text{ by commutative property } \\ (a+a+a-4a)+(b+b) \text{ by associative property } \\ a(1+1+1-4)+b(1+1) \text{ by distributive property } \\ a(-1)+b(2) \text{ by simplification } \\ -a+2b \text{ by commautive property }\]
anyways I be back I have thing
Wait you're leaving?! I thought you'd help me finish the problem??
@freckles COME BACK!!!!!
Math tease.
Sorry. I had something come up. Anyways I hoped the example helped.

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